Question: Solve for $x$ : $ 2|x + 10| + 8 = -3|x + 10| + 5 $
Explanation: Add $ {3|x + 10|} $ to both sides: $ \begin{eqnarray} 2|x + 10| + 8 &=& -3|x + 10| + 5 \\ \\ { + 3|x + 10|} && { + 3|x + 10|} \\ \\ 5|x + 10| + 8 &=& 5 \end{eqnarray} $ Subtract ${8}$ from both sides: $ \begin{eqnarray} 5|x + 10| + 8 &=& 5 \\ \\ { - 8} &=& { - 8} \\ \\ 5|x + 10| &=& -3 \end{eqnarray} $ Divide both sides by ${5}$ $ \dfrac{5|x + 10|} {{5}} = \dfrac{-3} {{5}} $ Simplify: $ |x + 10| = -\dfrac{3}{5}$ The absolute value cannot be negative. Therefore, there is no solution.